1 What is a Stochastic Process?.- 2 Results from Probability Theory.- 2.1 Introduction to probability theory.- 2.2 Bivariate distributions.- 2.3 Multivariate distributions.- 2.4 Probability generating functions.- 2.5 Characteristic functions.- 3 The Random Walk.- 3.1 The unrestricted random walk.- 3.2 Types of stochastic process.- 3.3 The gambler´s ruin.- 3.4 Generalisations of the random-walk model.- 4 Markov Chains.- 4.1 Definitions.- 4.2 Equilibrium distributions.- 4.3 Applications.- 4.4 Classification of the states of a Markov chain.- 5 The Poisson Process.- 6 Markov Chalns with Continuous Time Parameters.- 6.1 The theory.- 6.2 Applications.- 7 Non-Markov Processes in Continuous Time with Discrete State Spaces.- 7.1 Renewal theory.- 7.2 Population processes.- 7.3 Queuing theory.- 8 Diffusion Processes.- Recommendations For Further Reading.
1 What is a Stochastic Process?.- 2 Results from Probability Theory.- 2.1 Introduction to probability theory.- 2.2 Bivariate distributions.- 2.3 Multivariate distributions.- 2.4 Probability generating functions.- 2.5 Characteristic functions.- 3 The Random Walk.- 3.1 The unrestricted random walk.- 3.2 Types of stochastic process.- 3.3 The gambler's ruin.- 3.4 Generalisations of the random-walk model.- 4 Markov Chains.- 4.1 Definitions.- 4.2 Equilibrium distributions.- 4.3 Applications.- 4.4 Classification of the states of a Markov chain.- 5 The Poisson Process.- 6 Markov Chalns with Continuous Time Parameters.- 6.1 The theory.- 6.2 Applications.- 7 Non-Markov Processes in Continuous Time with Discrete State Spaces.- 7.1 Renewal theory.- 7.2 Population processes.- 7.3 Queuing theory.- 8 Diffusion Processes.- Recommendations For Further Reading.
Rodney Coleman lives close to Grenoble in France, where he is engaged in teaching and research. His interests include literature, bicycle riding and hiking in the mountains.
Inhaltsverzeichnis
1 What is a Stochastic Process?.- 2 Results from Probability Theory.- 2.1 Introduction to probability theory.- 2.2 Bivariate distributions.- 2.3 Multivariate distributions.- 2.4 Probability generating functions.- 2.5 Characteristic functions.- 3 The Random Walk.- 3.1 The unrestricted random walk.- 3.2 Types of stochastic process.- 3.3 The gambler's ruin.- 3.4 Generalisations of the random-walk model.- 4 Markov Chains.- 4.1 Definitions.- 4.2 Equilibrium distributions.- 4.3 Applications.- 4.4 Classification of the states of a Markov chain.- 5 The Poisson Process.- 6 Markov Chalns with Continuous Time Parameters.- 6.1 The theory.- 6.2 Applications.- 7 Non-Markov Processes in Continuous Time with Discrete State Spaces.- 7.1 Renewal theory.- 7.2 Population processes.- 7.3 Queuing theory.- 8 Diffusion Processes.- Recommendations For Further Reading.
Klappentext
1 What is a Stochastic Process?.- 2 Results from Probability Theory.- 2.1 Introduction to probability theory.- 2.2 Bivariate distributions.- 2.3 Multivariate distributions.- 2.4 Probability generating functions.- 2.5 Characteristic functions.- 3 The Random Walk.- 3.1 The unrestricted random walk.- 3.2 Types of stochastic process.- 3.3 The gambler¿s ruin.- 3.4 Generalisations of the random-walk model.- 4 Markov Chains.- 4.1 Definitions.- 4.2 Equilibrium distributions.- 4.3 Applications.- 4.4 Classification of the states of a Markov chain.- 5 The Poisson Process.- 6 Markov Chalns with Continuous Time Parameters.- 6.1 The theory.- 6.2 Applications.- 7 Non-Markov Processes in Continuous Time with Discrete State Spaces.- 7.1 Renewal theory.- 7.2 Population processes.- 7.3 Queuing theory.- 8 Diffusion Processes.- Recommendations For Further Reading.
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